Question

Find P(Blue bead).

a. $\frac{15}{36}$

b. $\frac{10}{36}$

c. $\frac{10}{12}$

d. $\frac{6}{36}$

Short answer

a.$\frac{15}{36}$

Step-by-step solution

Given information

This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y) and five blue (B) beads.

Explanation

Probability of Blue bead:

$$\begin{gathered} P(Bluebead)=P(HeadANDBluebeadinhead)+P(TailANDBluebeadintail) \\ P(Bluebead)=P\left(Head\right).P(Bluebeadinhead)+P\left(Tail\right).P(Bluebeadintail) \\ P(Bluebead)=\frac{2}{3}\times \frac{5}{12}+\frac{1}{3}\times \frac{5}{12} \\ P(Bluebead)=\frac{10}{36}+\frac{5}{36}=\frac{15}{36} \end{gathered}$$